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NASA NTRS2005

Medical and Scientific Evaluations aboard the KC-135. Microgravity-Compatible Flow Cytometer

A spaceflight-compatible flow cytometer would be useful for the diagnosis of astronaut illness during long duration spaceflight and for conducting in-flight research to evaluate the effects of microgravity on human physiology. Until recently, the primary limitations preventing the development of a spaceflight compatible flow cytometer have been largely mechanical. Standard commercially available flow cytometers are large, complex instruments that use high-energy lasers and require significant training to operate. Standard flow cytometers function by suspending the particles to be analyzed inside a sheath fluid for analysis. This requires the presence of several liters of sheath fluid for operation, and generates a corresponding amount of liquid hazardous waste. The particles are then passed through a flow cell which uses the fluid mechanical property of hydrodynamic focusing to place the cells in single-file (laminar flow) as they pass through a laser beam for scanning and evaluation. Many spaceflight experiments have demonstrated that fluid physics is dramatically altered in microgravity (MSF [Manned Space Flight] Fluid Physics Data Sheet-August 1997) and previous studies have shown that sheath-fluid based hydrodynamic focusing may also be altered during microgravity (Crucian et al, 2000). For these reasons it is likely that any spaceflight compatible design for a flow cytometer would abandon the sheath fluid requirement. The elimination of sheath fluid would remove both the problems of weight associated with large volumes of liquids as well as the large volume of liquid waste generated. It would also create the need for a method to create laminar particle flow distinct from the standard sheath-fluid based method. The spaceflight prototype instrument is based on a recently developed commercial flow cytometer possessing a novel flow cell design that creates single-particle laser scanning and evaluation without the need for sheath-fluid based hydrodynamic focusing. This instrument also possesses a number of design advances that make it conditionally microgravity compatible: it is highly miniaturized and lightweight, uses a low energy diode laser, has a small number of moving parts, does not use sheath fluid and does not generate significant liquid waste. Although possessing certain limitations, the commercial cytometer functions operationally like a standard bench top laboratory flow cytometer, aspirating liquid particle samples and generating histogram or dot-plot data in standard FCS file format. In its current configuration however, the cytometer is limited to three parameter/two-color capability (two color PMTs + forward scatter), does not allow compensation between colors, does not allow linear analysis and is operated by rather inflexible software with limited capabilities. This is due to the fact that the cytometer has been designed and marketed as an instrument specific to a few particular assays, not as a multipurpose cytometer.

Crucian, Brian↗

NASA NTRS2013

Studies of Inviscid Flux Schemes for Acoustics and Turbulence Problems

The last two decades have witnessed tremendous growth in computational power, the development of computational fluid dynamics (CFD) codes which scale well over thousands of processors, and the refinement of unstructured grid-generation tools which facilitate rapid surface and volume gridding of complex geometries. Thus, engineering calculations of 10(exp 7) - 10(exp 8) finite-volume cells have become routine for some types of problems. Although the Reynolds Averaged Navier Stokes (RANS) approach to modeling turbulence is still in extensive and wide use, increasingly large-eddy simulation (LES) and hybrid RANS-LES approaches are being applied to resolve the largest scales of turbulence in many engineering problems. However, it has also become evident that LES places different requirements on the numerical approaches for both the spatial and temporal discretization of the Navier Stokes equations than does RANS. In particular, LES requires high time accuracy and minimal intrinsic numerical dispersion and dissipation over a wide spectral range. In this paper, the performance of both central-difference and upwind-biased spatial discretizations is examined for a one-dimensional acoustic standing wave problem, the Taylor-Green vortex problem, and the turbulent channel fl ow problem.

Morris, C. I.↗

NASA NTRS2013

Studies of Inviscid Flux Schemes for Acoustics and Turbulence Problems

Morris, Christopher I.↗

NASA NTRSDate not supplied

Nearfield Summary and Analysis of the Third AIAA Sonic Boom Prediction Workshop C608 Low Boom Demonstrator

A summary and statistical analysis of the nearfield Computational Fluid Dynamics (CFD)submissions for the Third AIAA Sonic Boom Prediction Workshop is provided with a focus onthe C608 Low Boom Flight Test Demonstrator. The C608 is more complex in terms of geometryand propulsion boundary conditions than previous workshop cases and is more representativeof vehicles with lower ground loudness and the potential for lower annoyance. The nearfieldsignatures submitted by the participants are propagated to the ground to compute statisticsof loudness measures over the vehicle sonic boom carpet. Principle component analysis isused to extract the primary variation modes. Context from previous sonic boom workshopsindicates that this workshop has the lowest variation even though the case is more challengingbecause it is quieter and more complex. The results documented in this summary indicate thatthe international state-of-the-art for nearfield CFD has a variation that is small enough formeaningful low-boom design and analysis. Low-boom configuration analysis methods with lowvariation are important tools to develop certification processes for addressing the prohibitionon overland supersonic commercial flight.

sonic boom CFD workshop c608↗

DOE OSTI2017

Phase field model of fluid-driven fracture in elastic media: Immersed-fracture formulation and validation with analytical solutions

Propagation of fluid-driven fractures plays an important role in natural and engineering processes, including transport of magma in the lithosphere, geologic sequestration of carbon dioxide, and oil and gas recovery from low-permeability formations, among many others. The simulation of fracture propagation poses a computational challenge as a result of the complex physics of fracture and the need to capture disparate length scales. Phase field models represent fractures as a diffuse interface and enjoy the advantage that fracture nucleation, propagation, branching, or twisting can be simulated without ad hoc computational strategies like remeshing or local enrichment of the solution space. Here we propose a new quasi-static phase field formulation for modeling fluid-driven fracturing in elastic media at small strains. The approach fully couples the fluid flow in the fracture (described via the Reynolds lubrication approximation) and the deformation of the surrounding medium. The flow is solved on a lower dimensionality mesh immersed in the elastic medium. This approach leads to accurate coupling of both physics. We assessed the performance of the model extensively by comparing results for the evolution of fracture length, aperture, and fracture fluid pressure against analytical solutions under different fracture propagation regimes. Thus, the excellent performance of the numerical model in all regimes builds confidence in the applicability of phase field approaches to simulate fluid-driven fracture.

58 GEOSCIENCES↗

NASA NTRS2006

Shuttle Debris Impact Tool Assessment Using the Modern Design of Experiments

Computational tools have been developed to estimate thermal and mechanical reentry loads experienced by the Space Shuttle Orbiter as the result of cavities in the Thermal Protection System (TPS). Such cavities can be caused by impact from ice or insulating foam debris shed from the External Tank (ET) on liftoff. The reentry loads depend on cavity geometry and certain Shuttle state variables, among other factors. Certain simplifying assumptions have been made in the tool development about the cavity geometry variables. For example, the cavities are all modeled as shoeboxes , with rectangular cross-sections and planar walls. So an actual cavity is typically approximated with an idealized cavity described in terms of its length, width, and depth, as well as its entry angle, exit angle, and side angles (assumed to be the same for both sides). As part of a comprehensive assessment of the uncertainty in reentry loads estimated by the debris impact assessment tools, an effort has been initiated to quantify the component of the uncertainty that is due to imperfect geometry specifications for the debris impact cavities. The approach is to compute predicted loads for a set of geometry factor combinations sufficient to develop polynomial approximations to the complex, nonparametric underlying computational models. Such polynomial models are continuous and feature estimable, continuous derivatives, conditions that facilitate the propagation of independent variable errors. As an additional benefit, once the polynomial models have been developed, they require fewer computational resources to execute than the underlying finite element and computational fluid dynamics codes, and can generate reentry loads estimates in significantly less time. This provides a practical screening capability, in which a large number of debris impact cavities can be quickly classified either as harmless, or subject to additional analysis with the more comprehensive underlying computational tools. The polynomial models also provide useful insights into the sensitivity of reentry loads to various cavity geometry variables, and reveal complex interactions among those variables that indicate how the sensitivity of one variable depends on the level of one or more other variables. For example, the effect of cavity length on certain reentry loads depends on the depth of the cavity. Such interactions are clearly displayed in the polynomial response models.

DeLoach, R.↗

DOE OSTI2013

Large-Scale Spray Releases: Additional Aerosol Test Results

One of the events postulated in the hazard analysis for the Waste Treatment and Immobilization Plant (WTP) and other U.S. Department of Energy (DOE) nuclear facilities is a breach in process piping that produces aerosols with droplet sizes in the respirable range. The current approach for predicting the size and concentration of aerosols produced in a spray leak event involves extrapolating from correlations reported in the literature. These correlations are based on results obtained from small engineered spray nozzles using pure liquids that behave as a Newtonian fluid. The narrow ranges of physical properties on which the correlations are based do not cover the wide range of slurries and viscous materials that will be processed in the WTP and in processing facilities across the DOE complex. To expand the data set upon which the WTP accident and safety analyses were based, an aerosol spray leak testing program was conducted by Pacific Northwest National Laboratory (PNNL). PNNL’s test program addressed two key technical areas to improve the WTP methodology (Larson and Allen 2010). The first technical area was to quantify the role of slurry particles in small breaches where slurry particles may plug the hole and prevent high-pressure sprays. The results from an effort to address this first technical area can be found in Mahoney et al. (2012a). The second technical area was to determine aerosol droplet size distribution and total droplet volume from prototypic breaches and fluids, including sprays from larger breaches and sprays of slurries for which literature data are mostly absent. To address the second technical area, the testing program collected aerosol generation data at two scales, commonly referred to as small-scale and large-scale testing. The small-scale testing and resultant data are described in Mahoney et al. (2012b), and the large-scale testing and resultant data are presented in Schonewill et al. (2012). In tests at both scales, simulants were used to mimic the relevant physical properties projected for actual WTP process streams.

42 ENGINEERING↗

NASA NTRS1991

Analysis of minerals containing dissolved traces of the fluid phase components water and carbon dioxide

Substantial progress has been made towards a better understanding of the dissolution of common gas/fluid phase components, notably H2O and CO2, in minerals. It has been shown that the dissolution mechanisms are significantly more complex than currently believed. By judiciously combining various solid state analytical techniques, convincing evidence was obtained that traces of dissolved gas/fluid phase components undergo, at least in part, a redox conversion by which they split into reduced H2 and and reduced C on one hand and oxidized oxygen, O(-), on the other. Analysis for 2 and C as well as for any organic molecules which may form during the process of co-segregation are still impeded by the omnipresent danger of extraneous contamination. However, the presence of O(-), an unusual oxidized form of oxygen, has been proven beyond a reasonable doubt. The presence of O(-) testifies to the fact that a redox reaction must have taken place in the solid state involving the dissolved traces of gas/fluid phase components. Detailed information on the techniques used and the results obtained are given.

Freund, Friedemann↗

DOE OSTI2016

Infrastructure for Multiphysics Software Integration in High Performance Computing-Aided Science and Engineering

The project described in this report constructed and exercised an innovative multiphysics coupling toolkit called the Illinois Rocstar MultiPhysics Application Coupling Toolkit (IMPACT). IMPACT is an open source, flexible, natively parallel infrastructure for coupling multiple uniphysics simulation codes into multiphysics computational systems. IMPACT works with codes written in several high-performance-computing (HPC) programming languages, and is designed from the beginning for HPC multiphysics code development. It is designed to be minimally invasive to the individual physics codes being integrated, and has few requirements on those physics codes for integration. The goal of IMPACT is to provide the support needed to enable coupling existing tools together in unique and innovative ways to produce powerful new multiphysics technologies without extensive modification and rewrite of the physics packages being integrated. There are three major outcomes from this project: 1) construction, testing, application, and open-source release of the IMPACT infrastructure, 2) production of example open-source multiphysics tools using IMPACT, and 3) identification and engagement of interested organizations in the tools and applications resulting from the project. This last outcome represents the incipient development of a user community and application echosystem being built using IMPACT. Multiphysics coupling standardization can only come from organizations working together to define needs and processes that span the space of necessary multiphysics outcomes, which Illinois Rocstar plans to continue driving toward. The IMPACT system, including source code, documentation, and test problems are all now available through the public gitHUB.org system to anyone interested in multiphysics code coupling. Many of the basic documents explaining use and architecture of IMPACT are also attached as appendices to this document. Online HTML documentation is available through the gitHUB site. There are over 100 unit tests provided that run through the Illinois Rocstar Application Development (IRAD) lightweight testing infrastructure that is also supplied along with IMPACT. The package as a whole provides an excellent base for developing high-quality multiphysics applications using modern software development practices. To facilitate understanding how to utilize IMPACT effectively, two multiphysics systems have been developed and are available open-source through gitHUB. The simpler of the two systems, named ElmerFoamFSI in the repository, is a multiphysics, fluid-structure-interaction (FSI) coupling of the solid mechanics package Elmer with a fluid dynamics module from OpenFOAM. This coupling illustrates how to combine software packages that are unrelated by either author or architecture and combine them into a robust, parallel multiphysics system. A more complex multiphysics tool is the Illinois Rocstar Rocstar Multiphysics code that was rebuilt during the project around IMPACT. Rocstar Multiphysics was already an HPC multiphysics tool, but now that it has been rearchitected around IMPACT, it can be readily expanded to capture new and different physics in the future. In fact, during this project, the Elmer and OpenFOAM tools were also coupled into Rocstar Multiphysics and demonstrated. The full Rocstar Multiphysics codebase is also available on gitHUB, and licensed for any organization to use as they wish. Finally, the new IMPACT product is already being used in several multiphysics code coupling projects for the Air Force, NASA and the Missile Defense Agency, and initial work on expansion of the IMPACT-enabled Rocstar Multiphysics has begun in support of a commercial company. These initiatives promise to expand the interest and reach of IMPACT and Rocstar Multiphysics, ultimately leading to the envisioned standardization and consortium of users that was one of the goals of this project.

42 ENGINEERING↗

DOE OSTI2019

Liquid-State Dewetting of Pulsed-Laser-Heated Nanoscale Metal Films and Other Geometries

Metal films of nanoscale thickness, deposited on substrates and exposed to laser heating, provide systems that involve several interesting multiphysics effects. In addition to fluid mechanical aspects associated with a free boundary setup, other relevant physical effects include phase change, thermal flow, and liquid–solid interactions. Such films are challenging to model, in particular because inertial effects may be relevant, and large contact angles require care when considering the long-wave formulation. Applications of nanoscale metal films are numerous, and the materials science community is actively pursuing more complex setups involving templated films and substrates, bimetallic films and alloys, and a variety of elemental film geometries. The goal of this review is to discuss our current understanding of thin metal film systems, while also providing an overview of the challenges in this research area, which stands at the intersection of fluid mechanics, materials science, and thermal physics.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Wyoming CarbonSAFE: Advancing Commercialization of Low-Carbon Energy Technologies in Fossil-Rich Wyoming

Wyoming’s Powder River Basin (PRB) is the most prolific coal producer and exporter in the United States and the State of Wyoming’s largest oil-producing basin. In addition to being a leading energy producer, the PRB is the site of research programs whose aim is to develop and integrate low-carbon technologies into existing fossil fuel energy industries. Much of the PRB’s low-carbon research is focused around Dry Fork Station (DFS), which is the newest coal-fired power station in the western US. Currently, DFS hosts five carbon capture projects, including pilot-scale capture projects that utilize different capture technologies and a full front-end engineering and design (FEED) study, a commercial CO 2 pipeline for nearby CO 2 -enhanced oil recovery industry, and is also co-located with the Wyoming Integrated Test Center, which is a host facility for unconventional carbon utilization research (i.e. flue gas carbon-to-products innovations). DFS is also the host site for the Wyoming CarbonSAFE project. Wyoming CarbonSAFE, funded by the Department of Energy/National Energy Technology Laboratory, is a multi-phased program (currently in Phase II) whose core objective is developing and validating storage sites within a complex capable of storing 50 million metric tonnes of CO 2 over a 30 year project period using carbon capture, utilization and storage (CCUS). This paper will provide an overview of the project to-date, showing that CarbonSAFE goals are achievable with respect to geologic, environmental, regulatory, CO 2 source and economic conditions, and why the State of Wyoming offers one of the more favorable environments to advance the commercialization studies. In 2019, the project team designed and completed a ~10,000 foot stratigraphic test well just south of DFS. From this well, the team collected over 600 feet of core, fluid samples from target injection zones, and a full petrophysical log suite. In addition, legacy 2D seismic lines were acquired and a 3D seismic survey was acquired in the fall of 2020. The objective of these field activities has been to identify and characterize target storage reservoirs and associated caprock. This complex has several reservoirs that could meet commercial injection goals, and over 4000 feet of associated caprock. Simulations of site performance suggest that stacked injection provides the most effective storage strategy, and would necessitate several sites within the greater complex to meet final project injection goals. Other work within this project includes the development of a business-case around proximal fields with CO 2 -enhanced oil recovery potential and existing tax credits, assessment of regulatory conditions, including pore space ownership and Class VI injection well permitting requirements, implementation of a robust public outreach Electronic copy available at: https://ssrn.com/abstract=3821220 GHGT-15 McLaughlin 2 program, and surface site characterization activities that have focused on environmental factors. In the PRB and at DFS, the State of Wyoming and other entities have made carbon management a priority of its future energy industry by providing a regulatory and business framework that is favorable to advancing these technologies. These endeavors will become more realistic with the successful implementation of Wyoming CarbonSAFE, and its ability to secure and validate commercial-scale CCUS at the center of Wyoming’s premier low-carbon research efforts.

McLaughlin, Fred↗

NASA NTRS1991

FAST: A multi-processed environment for visualization of computational fluid dynamics

Three-dimensional, unsteady, multi-zoned fluid dynamics simulations over full scale aircraft are typical of the problems being investigated at NASA Ames' Numerical Aerodynamic Simulation (NAS) facility on CRAY2 and CRAY-YMP supercomputers. With multiple processor workstations available in the 10-30 Mflop range, we feel that these new developments in scientific computing warrant a new approach to the design and implementation of analysis tools. These larger, more complex problems create a need for new visualization techniques not possible with the existing software or systems available as of this writing. The visualization techniques will change as the supercomputing environment, and hence the scientific methods employed, evolves even further. The Flow Analysis Software Toolkit (FAST), an implementation of a software system for fluid mechanics analysis, is discussed.

Bancroft, Gordon V.↗

DOE OSTI2015

Trajectory approach to the Schrödinger–Langevin equation with linear dissipation for ground states

The Schrödinger–Langevin equation with linear dissipation is integrated by propagating an ensemble of Bohmian trajectories for the ground state of quantum systems. Substituting the wave function expressed in terms of the complex action into the Schrödinger–Langevin equation yields the complex quantum Hamilton–Jacobi equation with linear dissipation. We transform this equation into the arbitrary Lagrangian–Eulerian version with the grid velocity matching the flow velocity of the probability fluid. The resulting equation is simultaneously integrated with the trajectory guidance equation. Then, the computational method is applied to the harmonic oscillator, the double well potential, and the ground vibrational state of methyl iodide. The excellent agreement between the computational and the exact results for the ground state energies and wave functions shows that this study provides a synthetic trajectory approach to the ground state of quantum systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Mechanistic Study of Controlled Zinc Electrodeposition Behaviors Facilitated by Nanoscale Electrolyte Additives at the Electrode Interface

Nanoparticle organic hybrid materials (NOHMs) are liquid-like materials composed of an inorganic core to which a polymeric canopy is ionically tethered. NOHMs have unique properties including negligible vapor pressure, high oxidative thermal stability, and the ability to bind to reactive species of interest due to the tunability of their polymeric canopy. This makes them promising multifunctional materials for a wide range of energy and environmental technologies, including electrolyte additives for electrochemical energy storage (e.g., flow batteries) and the electrochemical conversion of CO 2 to chemicals and fuels. Due to their unique transport behaviors in fluid systems, an understanding of the near-electrode surface behavior of NOHMs in electrolyte solutions and their effect on electrochemical reactions is still lacking. In this work, the complexation of zinc (Zn) by NOHMs with an ionically tethered polyetheramine canopy (HPE) (NOHM-I-HPE) was studied using attenuated total reflectance Fourier transform infrared and Carbon-13 nuclear magnetic resonance spectroscopy. Additionally, various electrochemical techniques were employed to discern the role of NOHM-I-HPE during zinc electrodeposition, and the results were compared to those of the electrochemical system containing untethered HPE polymers. Our findings confirmed that NOHM-I-HPE and HPE reversibly complex zinc in the aqueous electrolyte. NOHM-I-HPE and HPE were found to block some of the electrode active sites, reducing the overall current density during electrodeposition, while facilitating the formation of smooth zinc deposits, as revealed by surface imaging and diffraction techniques. Observed variations in the current density responses and the degree of passivation created by the NOHM-I-HPE and HPE adsorbed on the electrode surface revealed that their different packing behaviors at the electrode–electrolyte interface influence the zinc deposition mechanism. The presence of the nanoparticle and ordering offered by the NOHMs as well as the structured conformation of the polymeric canopy allowed the formation of void spaces and free volumes for enhanced transport behaviors. Furthermore, these findings provided insights into how structured electrolyte additives such as NOHMs can allow for advancements in electrolyte design for controlled deposition of metal species from energy-dense electrolytes or for other electrochemical reactions.

25 ENERGY STORAGE↗

DOE OSTI2013

Dynamic Interaction Between Membrane-Bound Full-Length Cytochrome P450 and Cytochrome b 5 Observed by Solid-State NMR Spectroscopy

Microsomal monoxygenase enzymes of the cytochrome-P450 family are found in all biological kingdoms, and play a central role in the breakdown of metabolic as well as xenobiotic, toxic and 70% of the drugs in clinical use. Full-length cytochrome-b5 has been shown to be important for the catalytic activity of cytochrome-P450. Despite the significance in understanding the interactions between these two membrane-associated proteins, only limited high-resolution structural information on the full-length cytochrome-P450 and the cytochromes-b5-P450 complex is available. Here, we report a structural study on a functional ,72-kDa cytochromes-b5-P450 complex embedded in magnetically-aligned bicelles without having to freeze the sample. Functional and solid-state NMR (Nuclear Magnetic Resonance) data reveal interactions between the proteins in fluid lamellar phase bilayers. In addition, our data infer that the backbone structure and geometry of the transmembrane domain of cytochrome-b5 is not significantly altered due to its interaction with cytochrome-P450, whereas the mobility of cytochrome-b5 is considerably reduced.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Existence domains of slow and fast ion-acoustic solitons in two-ion space plasmas

A study of large amplitude ion-acoustic solitons is conducted for a model composed of cool and hot ions and cool and hot electrons. Using the Sagdeev pseudo-potential formalism, the scope of earlier studies is extended to consider why upper Mach number limitations arise for slow and fast ion-acoustic solitons. Treating all plasma constituents as adiabatic fluids, slow ion-acoustic solitons are limited in the order of increasing cool ion concentrations by the number densities of the cool, and then the hot ions becoming complex valued, followed by positive and then negative potential double layer regions. Only positive potentials are found for fast ion-acoustic solitons which are limited only by the hot ion number density having to remain real valued. The effect of neglecting as opposed to including inertial effects of the hot electrons is found to induce only minor quantitative changes in the existence regions of slow and fast ion-acoustic solitons.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2014

Living liquid crystals

Collective motion of self-propelled organisms or synthetic particles, often termed •active fluid,• has attracted enormous attention in the broad scientific community because of its fundamentally nonequilibrium nature. Energy input and interactions among the moving units and the medium lead to complex dynamics. Here,we introduce a class of active matter-living liquid crystals (UCs} that combines living swimming bacteria with a lyotropic liquid crystal. The physical properties of LLCs can be controlled by the amount of oxygen available to bacteria, by concentration of ingredients, or by temperature. Our studies reveal a wealth of intriguing dynamic phenomena. caused by the coupling between the activity-triggered flow and long-range orientational order of the medium. Among these are (i) nonlinear trajectories of bacterial motion guided by nonuniform director, (ii) local melting of the liquid crystal caused by the bacteria-produced shear flows, (iii) activity-triggered transition from a nonflowing uniform state into a flowing one-dimensional periodic pattern and its evolution into a turbulent array of topological defects, and (iv) birefringence enabled visualization of microflow generated by the nanometers thick bacterial flagella. Unlike their isotropic counterpart, the LLCs show collective dynamic effects at very low volume fraction of bacteria, on the order of 0.2%. Our work suggests an unorthodox design concept to control and manipulate the dynamic behavior of soft active matter and opens the door for potential biosensing and biomedical applications.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Forecasting high-dimensional spatio-temporal systems from sparse measurements

This paper introduces a new neural network architecture designed to forecast high-dimensional spatio-temporal data using only sparse measurements. The architecture uses a two-stage end-to-end framework that combines neural ordinary differential equations (NODEs) with vision transformers. Initially, our approach models the underlying dynamics of complex systems within a low-dimensional space; and then it reconstructs the corresponding high-dimensional spatial fields. Many traditional methods involve decoding high-dimensional spatial fields before modeling the dynamics, while some other methods use an encoder to transition from high-dimensional observations to a latent space for dynamic modeling. In contrast, our approach directly uses sparse measurements to model the dynamics, bypassing the need for an encoder. This direct approach simplifies the modeling process, reduces computational complexity, and enhances the efficiency and scalability of the method for large datasets. We demonstrate the effectiveness of our framework through applications to various spatio-temporal systems, including fluid flows and global weather patterns. Although sparse measurements have limitations, our experiments reveal that they are sufficient to forecast system dynamics accurately over long time horizons. Our results also indicate that the performance of our proposed method remains robust across different sensor placement strategies, with further improvements as the number of sensors increases. This robustness underscores the flexibility of our architecture, particularly in real-world scenarios where sensor data is often sparse and unevenly distributed.

97 MATHEMATICS AND COMPUTING↗